1. Ensure that you have **Threaded Comments** enabled: go to `Dashboard -> Settings -> Discussion` and enable the option to thread comments
2. Ensure that your Theme **enqueues the `comment-reply` script**. Look for the following, usually in `header.php`, `functions.php`, etc.:

        <?php wp_enqueue_script( 'comment-reply' ); ?>

    Note: this call is usually wrapped in a conditional, such as:

        <?php
        if ( is_single() && comments_open() && get_option( 'thread_comments' ) ) {
            wp_enqueue_script( 'comment-reply' );
        }
        ?>
    
    Note 2: You may also see this code inside of a *callback*, hooked into `wp_enqueue_scripts`, `wp_head`, or `comment_form_before`

### Edit ###

To enqueue the comment-reply script via `functions.php, don't just put `<?php wp_enqueue_script( 'comment-reply' ); ?>`. That's `_doing_it_wrong()`, because it will fire far too eary. Do this instead:

    <?php
    function wpse52737_enqueue_comment_reply_script() {
        if ( get_option( 'thread_comments' ) ) {
            wp_enqueue_script( 'comment_reply' );
        }
    }
    add_action( 'comment_form_before', 'wpse52737_enqueue_comment_reply_script' );
    ?>